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[CrossRef]
[PubMed]

M. Petrou and A. Giannakidis, “Complete tomographic reconstruction of 2-d vector fields using a system of linear equations,” Proceedings of the 12th Annual Medical Image Understanding and Analysis Conference (MIUA 2008) July 2-3, 2008, Dundee, Scotland, UK, pp. 132–136.

C. Habermann and F. Kindermann, “Multidimensional spline interpolation: Theory and applications,” Comput. Econ. 30, 153–169(2007).

[CrossRef]

A. Kadyrov and M. Petrou, “Affine parameter estimation from the trace transform,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 1631–1645(2006).

[CrossRef]
[PubMed]

T. D. Sanger, J. Kaiser, and B. Placek, “Reaching movements in childhood dystonia contain signal-dependent noise,” J. Child Neurol. 20, 489–496(2005).

[PubMed]

M. Petrou and A. Kadyrov, “Affine invariant features from the trace transform,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 30–44(2004).

[CrossRef]
[PubMed]

I. N. Bronshtein, K. A. Semendyayev, G. Musiol, and H. Muehlig, Handbook of Mathematics (Springer, 2003).

D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing(American Mathematical Society, 2002).

G. Krüger and G. H. Glover, “Physiological noise in oxygenation-sensitive magnetic resonance imaging,” Magn. Reson. Med. 46, 631–677(2001).

[CrossRef]
[PubMed]

H. Aben and A. Puro, “Photoelastic tomography for three-dimensional flow birefringence studies,” Inverse Probl. 13, 215–221(1997).

[CrossRef]

N. P. Efremov, N. P. Poluektov, and V. N. Kharchenko, “Tomography of ion and atom velocities in plasmas,” J. Quant. Spectrosc. Radiat. Transf. 53, 723–728(1995).

[CrossRef]

M. Zahn, “Transform relationship between Kerr-effect optical phase shift and non-uniform electric field distributions,” IEEE Trans. Dielectr. Electr. Insul. 1, 235–246(1994).

[CrossRef]

A. Schwarz, “Three-dimensional reconstruction of temperature and velocity fields in a furnace,” Proceedings of ECAPT, The European Concerted Action on Process Tomography (International Society for Industrial Process Tomography, 1994), pp. 227–233.

K. B. Winters and D. Rouseff, “Tomographic reconstruction of stratified fluid flow,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 40, 26–33(1993).

[CrossRef]
[PubMed]

S. P. Juhlin, “Doppler tomography,” Proceedings of the 15th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, October 28–31, 1993, San Diego, California, USA (1993) pp. 212–213.

[CrossRef]

S. J. Norton, “Unique tomographic reconstruction of vector fields using boundary data,” IEEE Trans. Image Process. 1, 406–412 (1992).

[CrossRef]
[PubMed]

V. A. Sharafutdinov, “Tomographic problem of photoelasticity,” Proc. SPIE 1843, 234–243(1992).

[CrossRef]

P. Juhlin, “Principles of Doppler Tomography,” Lund Institute of Technology, Sweden, Department of Mathematics, LUTFD2/(TFMA-92)/7002+17P, August (1992).

H. Schwetlick and H. Kretzschmar, Numerische Verfahren fur Naturwissenschaftler und Ingenieure (Fachbuchverlag, 1991).

H. Braun and A. Hauck, “Tomographic reconstruction of vector fields,” IEEE Trans. Signal Process. 39, 464–471(1991).

[CrossRef]

D. Rouseff, K. B. Winters, and T. E. Ewart, “Reconstruction of oceanic microstructure by tomography: a numerical feasibility study,” J. Geophys. Res. 96, 8823–8833(1991).

[CrossRef]

K. B. Winters and D. Rouseff, “A filtered backprojection method for the tomographic reconstruction of fluid vorticity,” Inverse Probl. 6, L33–L38(1990).

[CrossRef]

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, 1983).

W. Munk and C. Wunsch, “Observing the ocean in the 1990s,” Philos. Trans. R. Soc. London, Ser. A 307, 439–464 (1982).

[CrossRef]

S. J. Norton and M. Linzer, “Correcting for ray refraction in velocity and attenuation tomography: a perturbation approach,” Ultrason. Imaging 4, 201–233(1982).

[CrossRef]
[PubMed]

D. M. Kramer and P. C. Lauterbur, “On the problem of reconstructing images of non-scalar parameters from projections. Applications to vector fields,” ISA Trans. 26, 2674–2677(1979).

[CrossRef]

S. E. Segre, “The measurement of poloidal magnetic field in a tokamak by the change of polarization of an electromagnetic wave,” Plasma Phys. 20, 295–307(1978).

[CrossRef]

C. de Boor, A Practical Guide to Splines (Springer-Verlag, 1978).

[CrossRef]

S. A. Johnson, J. F. Greenleaf, M. Tanaka, and G. Flandro, “Reconstructing three-dimensional temperature and fluid velocity vector fields from acoustic transmission measurements,” ISA Trans. 16, 3, pp. 3–15, 1977.

H. Aben and A. Puro, “Photoelastic tomography for three-dimensional flow birefringence studies,” Inverse Probl. 13, 215–221(1997).

[CrossRef]

H. Braun and A. Hauck, “Tomographic reconstruction of vector fields,” IEEE Trans. Signal Process. 39, 464–471(1991).

[CrossRef]

I. N. Bronshtein, K. A. Semendyayev, G. Musiol, and H. Muehlig, Handbook of Mathematics (Springer, 2003).

D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing(American Mathematical Society, 2002).

C. de Boor, A Practical Guide to Splines (Springer-Verlag, 1978).

[CrossRef]

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, 1983).

N. P. Efremov, N. P. Poluektov, and V. N. Kharchenko, “Tomography of ion and atom velocities in plasmas,” J. Quant. Spectrosc. Radiat. Transf. 53, 723–728(1995).

[CrossRef]

D. Rouseff, K. B. Winters, and T. E. Ewart, “Reconstruction of oceanic microstructure by tomography: a numerical feasibility study,” J. Geophys. Res. 96, 8823–8833(1991).

[CrossRef]

S. A. Johnson, J. F. Greenleaf, M. Tanaka, and G. Flandro, “Reconstructing three-dimensional temperature and fluid velocity vector fields from acoustic transmission measurements,” ISA Trans. 16, 3, pp. 3–15, 1977.

M. Petrou and A. Giannakidis, “Complete tomographic reconstruction of 2-d vector fields using a system of linear equations,” Proceedings of the 12th Annual Medical Image Understanding and Analysis Conference (MIUA 2008) July 2-3, 2008, Dundee, Scotland, UK, pp. 132–136.

G. Krüger and G. H. Glover, “Physiological noise in oxygenation-sensitive magnetic resonance imaging,” Magn. Reson. Med. 46, 631–677(2001).

[CrossRef]
[PubMed]

S. A. Johnson, J. F. Greenleaf, M. Tanaka, and G. Flandro, “Reconstructing three-dimensional temperature and fluid velocity vector fields from acoustic transmission measurements,” ISA Trans. 16, 3, pp. 3–15, 1977.

C. Habermann and F. Kindermann, “Multidimensional spline interpolation: Theory and applications,” Comput. Econ. 30, 153–169(2007).

[CrossRef]

H. Braun and A. Hauck, “Tomographic reconstruction of vector fields,” IEEE Trans. Signal Process. 39, 464–471(1991).

[CrossRef]

B. M. Howe, P. F. Worcester, and R. C. Spindel, “Ocean acoustic tomography: Mesoscale velocity,” J. Geophys. Res. 92, 3785–3806 (1987).

[CrossRef]

S. A. Johnson, J. F. Greenleaf, M. Tanaka, and G. Flandro, “Reconstructing three-dimensional temperature and fluid velocity vector fields from acoustic transmission measurements,” ISA Trans. 16, 3, pp. 3–15, 1977.

P. Juhlin, “Principles of Doppler Tomography,” Lund Institute of Technology, Sweden, Department of Mathematics, LUTFD2/(TFMA-92)/7002+17P, August (1992).

S. P. Juhlin, “Doppler tomography,” Proceedings of the 15th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, October 28–31, 1993, San Diego, California, USA (1993) pp. 212–213.

[CrossRef]

A. Kadyrov and M. Petrou, “Affine parameter estimation from the trace transform,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 1631–1645(2006).

[CrossRef]
[PubMed]

M. Petrou and A. Kadyrov, “Affine invariant features from the trace transform,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 30–44(2004).

[CrossRef]
[PubMed]

T. D. Sanger, J. Kaiser, and B. Placek, “Reaching movements in childhood dystonia contain signal-dependent noise,” J. Child Neurol. 20, 489–496(2005).

[PubMed]

N. P. Efremov, N. P. Poluektov, and V. N. Kharchenko, “Tomography of ion and atom velocities in plasmas,” J. Quant. Spectrosc. Radiat. Transf. 53, 723–728(1995).

[CrossRef]

D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing(American Mathematical Society, 2002).

C. Habermann and F. Kindermann, “Multidimensional spline interpolation: Theory and applications,” Comput. Econ. 30, 153–169(2007).

[CrossRef]

D. M. Kramer and P. C. Lauterbur, “On the problem of reconstructing images of non-scalar parameters from projections. Applications to vector fields,” ISA Trans. 26, 2674–2677(1979).

[CrossRef]

H. Schwetlick and H. Kretzschmar, Numerische Verfahren fur Naturwissenschaftler und Ingenieure (Fachbuchverlag, 1991).

G. Krüger and G. H. Glover, “Physiological noise in oxygenation-sensitive magnetic resonance imaging,” Magn. Reson. Med. 46, 631–677(2001).

[CrossRef]
[PubMed]

D. M. Kramer and P. C. Lauterbur, “On the problem of reconstructing images of non-scalar parameters from projections. Applications to vector fields,” ISA Trans. 26, 2674–2677(1979).

[CrossRef]

S. J. Norton and M. Linzer, “Correcting for ray refraction in velocity and attenuation tomography: a perturbation approach,” Ultrason. Imaging 4, 201–233(1982).

[CrossRef]
[PubMed]

I. N. Bronshtein, K. A. Semendyayev, G. Musiol, and H. Muehlig, Handbook of Mathematics (Springer, 2003).

W. Munk and C. Wunsch, “Observing the ocean in the 1990s,” Philos. Trans. R. Soc. London, Ser. A 307, 439–464 (1982).

[CrossRef]

I. N. Bronshtein, K. A. Semendyayev, G. Musiol, and H. Muehlig, Handbook of Mathematics (Springer, 2003).

S. J. Norton, “Unique tomographic reconstruction of vector fields using boundary data,” IEEE Trans. Image Process. 1, 406–412 (1992).

[CrossRef]
[PubMed]

S. J. Norton, “Tomographic reconstruction of 2-D vector fields: Application to flow imaging,” Geophys. J. Int. 97, 161–168 (1988).

[CrossRef]

S. J. Norton and M. Linzer, “Correcting for ray refraction in velocity and attenuation tomography: a perturbation approach,” Ultrason. Imaging 4, 201–233(1982).

[CrossRef]
[PubMed]

M. Petrou and A. Giannakidis, “Complete tomographic reconstruction of 2-d vector fields using a system of linear equations,” Proceedings of the 12th Annual Medical Image Understanding and Analysis Conference (MIUA 2008) July 2-3, 2008, Dundee, Scotland, UK, pp. 132–136.

A. Kadyrov and M. Petrou, “Affine parameter estimation from the trace transform,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 1631–1645(2006).

[CrossRef]
[PubMed]

M. Petrou and A. Kadyrov, “Affine invariant features from the trace transform,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 30–44(2004).

[CrossRef]
[PubMed]

T. D. Sanger, J. Kaiser, and B. Placek, “Reaching movements in childhood dystonia contain signal-dependent noise,” J. Child Neurol. 20, 489–496(2005).

[PubMed]

N. P. Efremov, N. P. Poluektov, and V. N. Kharchenko, “Tomography of ion and atom velocities in plasmas,” J. Quant. Spectrosc. Radiat. Transf. 53, 723–728(1995).

[CrossRef]

H. Aben and A. Puro, “Photoelastic tomography for three-dimensional flow birefringence studies,” Inverse Probl. 13, 215–221(1997).

[CrossRef]

K. B. Winters and D. Rouseff, “Tomographic reconstruction of stratified fluid flow,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 40, 26–33(1993).

[CrossRef]
[PubMed]

D. Rouseff, K. B. Winters, and T. E. Ewart, “Reconstruction of oceanic microstructure by tomography: a numerical feasibility study,” J. Geophys. Res. 96, 8823–8833(1991).

[CrossRef]

K. B. Winters and D. Rouseff, “A filtered backprojection method for the tomographic reconstruction of fluid vorticity,” Inverse Probl. 6, L33–L38(1990).

[CrossRef]

T. D. Sanger, J. Kaiser, and B. Placek, “Reaching movements in childhood dystonia contain signal-dependent noise,” J. Child Neurol. 20, 489–496(2005).

[PubMed]

A. Schwarz, “Three-dimensional reconstruction of temperature and velocity fields in a furnace,” Proceedings of ECAPT, The European Concerted Action on Process Tomography (International Society for Industrial Process Tomography, 1994), pp. 227–233.

H. R. Schwarz, Numerische Mathematik (B. G. Teubner, 1986).

H. Schwetlick and H. Kretzschmar, Numerische Verfahren fur Naturwissenschaftler und Ingenieure (Fachbuchverlag, 1991).

S. E. Segre, “The measurement of poloidal magnetic field in a tokamak by the change of polarization of an electromagnetic wave,” Plasma Phys. 20, 295–307(1978).

[CrossRef]

I. N. Bronshtein, K. A. Semendyayev, G. Musiol, and H. Muehlig, Handbook of Mathematics (Springer, 2003).

V. A. Sharafutdinov, “Tomographic problem of photoelasticity,” Proc. SPIE 1843, 234–243(1992).

[CrossRef]

B. M. Howe, P. F. Worcester, and R. C. Spindel, “Ocean acoustic tomography: Mesoscale velocity,” J. Geophys. Res. 92, 3785–3806 (1987).

[CrossRef]

S. A. Johnson, J. F. Greenleaf, M. Tanaka, and G. Flandro, “Reconstructing three-dimensional temperature and fluid velocity vector fields from acoustic transmission measurements,” ISA Trans. 16, 3, pp. 3–15, 1977.

K. B. Winters and D. Rouseff, “Tomographic reconstruction of stratified fluid flow,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 40, 26–33(1993).

[CrossRef]
[PubMed]

D. Rouseff, K. B. Winters, and T. E. Ewart, “Reconstruction of oceanic microstructure by tomography: a numerical feasibility study,” J. Geophys. Res. 96, 8823–8833(1991).

[CrossRef]

K. B. Winters and D. Rouseff, “A filtered backprojection method for the tomographic reconstruction of fluid vorticity,” Inverse Probl. 6, L33–L38(1990).

[CrossRef]

B. M. Howe, P. F. Worcester, and R. C. Spindel, “Ocean acoustic tomography: Mesoscale velocity,” J. Geophys. Res. 92, 3785–3806 (1987).

[CrossRef]

W. Munk and C. Wunsch, “Observing the ocean in the 1990s,” Philos. Trans. R. Soc. London, Ser. A 307, 439–464 (1982).

[CrossRef]

M. Zahn, “Transform relationship between Kerr-effect optical phase shift and non-uniform electric field distributions,” IEEE Trans. Dielectr. Electr. Insul. 1, 235–246(1994).

[CrossRef]

H. M. Hertz, “Kerr effect tomography for nonintrusive spatially resolved measurements of asymmetric electric field distributions,” Appl. Opt. 25, 914–921(1986).

[CrossRef]
[PubMed]

H. K. Aben, “Kerr effect tomography for general axisymmetric field,” Appl. Opt. 26, 2921–2924(1987).

[CrossRef]
[PubMed]

G. W. Faris and R. L. Byer, “Three-dimensional beam-deflection optical tomography of a supersonic jet,” Appl. Opt. 27, 5202–5212(1988).

[CrossRef]
[PubMed]

R. M. Rangayyan, M. Ciuc, and F. Faghih, “Adapted-neighborhood filtering of images corrupted by signal-dependent noise,” Appl. Opt. 37, 4477–4487(1998).

[CrossRef]

C. Habermann and F. Kindermann, “Multidimensional spline interpolation: Theory and applications,” Comput. Econ. 30, 153–169(2007).

[CrossRef]

S. J. Norton, “Tomographic reconstruction of 2-D vector fields: Application to flow imaging,” Geophys. J. Int. 97, 161–168 (1988).

[CrossRef]

M. Zahn, “Transform relationship between Kerr-effect optical phase shift and non-uniform electric field distributions,” IEEE Trans. Dielectr. Electr. Insul. 1, 235–246(1994).

[CrossRef]

S. J. Norton, “Unique tomographic reconstruction of vector fields using boundary data,” IEEE Trans. Image Process. 1, 406–412 (1992).

[CrossRef]
[PubMed]

M. Petrou and A. Kadyrov, “Affine invariant features from the trace transform,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 30–44(2004).

[CrossRef]
[PubMed]

A. Kadyrov and M. Petrou, “Affine parameter estimation from the trace transform,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 1631–1645(2006).

[CrossRef]
[PubMed]

H. Braun and A. Hauck, “Tomographic reconstruction of vector fields,” IEEE Trans. Signal Process. 39, 464–471(1991).

[CrossRef]

K. B. Winters and D. Rouseff, “Tomographic reconstruction of stratified fluid flow,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 40, 26–33(1993).

[CrossRef]
[PubMed]

K. B. Winters and D. Rouseff, “A filtered backprojection method for the tomographic reconstruction of fluid vorticity,” Inverse Probl. 6, L33–L38(1990).

[CrossRef]

H. Aben and A. Puro, “Photoelastic tomography for three-dimensional flow birefringence studies,” Inverse Probl. 13, 215–221(1997).

[CrossRef]

S. A. Johnson, J. F. Greenleaf, M. Tanaka, and G. Flandro, “Reconstructing three-dimensional temperature and fluid velocity vector fields from acoustic transmission measurements,” ISA Trans. 16, 3, pp. 3–15, 1977.

D. M. Kramer and P. C. Lauterbur, “On the problem of reconstructing images of non-scalar parameters from projections. Applications to vector fields,” ISA Trans. 26, 2674–2677(1979).

[CrossRef]

T. D. Sanger, J. Kaiser, and B. Placek, “Reaching movements in childhood dystonia contain signal-dependent noise,” J. Child Neurol. 20, 489–496(2005).

[PubMed]

D. Rouseff, K. B. Winters, and T. E. Ewart, “Reconstruction of oceanic microstructure by tomography: a numerical feasibility study,” J. Geophys. Res. 96, 8823–8833(1991).

[CrossRef]

B. M. Howe, P. F. Worcester, and R. C. Spindel, “Ocean acoustic tomography: Mesoscale velocity,” J. Geophys. Res. 92, 3785–3806 (1987).

[CrossRef]

N. P. Efremov, N. P. Poluektov, and V. N. Kharchenko, “Tomography of ion and atom velocities in plasmas,” J. Quant. Spectrosc. Radiat. Transf. 53, 723–728(1995).

[CrossRef]

G. Krüger and G. H. Glover, “Physiological noise in oxygenation-sensitive magnetic resonance imaging,” Magn. Reson. Med. 46, 631–677(2001).

[CrossRef]
[PubMed]

W. Munk and C. Wunsch, “Observing the ocean in the 1990s,” Philos. Trans. R. Soc. London, Ser. A 307, 439–464 (1982).

[CrossRef]

S. E. Segre, “The measurement of poloidal magnetic field in a tokamak by the change of polarization of an electromagnetic wave,” Plasma Phys. 20, 295–307(1978).

[CrossRef]

V. A. Sharafutdinov, “Tomographic problem of photoelasticity,” Proc. SPIE 1843, 234–243(1992).

[CrossRef]

S. J. Norton and M. Linzer, “Correcting for ray refraction in velocity and attenuation tomography: a perturbation approach,” Ultrason. Imaging 4, 201–233(1982).

[CrossRef]
[PubMed]

S. P. Juhlin, “Doppler tomography,” Proceedings of the 15th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, October 28–31, 1993, San Diego, California, USA (1993) pp. 212–213.

[CrossRef]

P. Juhlin, “Principles of Doppler Tomography,” Lund Institute of Technology, Sweden, Department of Mathematics, LUTFD2/(TFMA-92)/7002+17P, August (1992).

M. Petrou and A. Giannakidis, “Complete tomographic reconstruction of 2-d vector fields using a system of linear equations,” Proceedings of the 12th Annual Medical Image Understanding and Analysis Conference (MIUA 2008) July 2-3, 2008, Dundee, Scotland, UK, pp. 132–136.

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, 1983).

D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing(American Mathematical Society, 2002).

H. R. Schwarz, Numerische Mathematik (B. G. Teubner, 1986).

H. Schwetlick and H. Kretzschmar, Numerische Verfahren fur Naturwissenschaftler und Ingenieure (Fachbuchverlag, 1991).

I. N. Bronshtein, K. A. Semendyayev, G. Musiol, and H. Muehlig, Handbook of Mathematics (Springer, 2003).

C. de Boor, A Practical Guide to Splines (Springer-Verlag, 1978).

[CrossRef]

A. Schwarz, “Three-dimensional reconstruction of temperature and velocity fields in a furnace,” Proceedings of ECAPT, The European Concerted Action on Process Tomography (International Society for Industrial Process Tomography, 1994), pp. 227–233.